Use the image to answer the question.
An illustration shows three rays passing through three points from a common origin point at upper S. Point upper T is to the horizontal left of upper S. A ray from upper S joins upper T with an arrow near upper T. Point upper V is on the top inclined to the right of point upper S. A ray from upper S joins upper V with an arrow near upper V. Point upper R is to top right of point upper S, below point upper V. A ray from upper S joins upper R with an arrow near upper R. Angle upper T upper S upper R is labeled as 157 degrees. Angle upper V upper S upper R as 54 degrees.
What is the measure of ∠TSV ?
(1 point)
°
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The measure of angle TSV can be calculated by subtracting the measures of angles TSR and VSR from 180 degrees, since the three angles form a straight line.
180 - 157 - 54 = 31 degrees
Therefore, the measure of angle TSV is 31 degrees.
Use the image to answer the question.
An illustration shows three rays from a common vertex with labeled angles. The first ray is inclined to the horizontal left of the common vertex with an arrow at the end. The second ray is inclined to the horizontal right of the common vertex with an arrow at the end. The third ray is to the top right of the common vertex with an arrow at the end. It is between the other two rays. The angle between the first and the third rays is labeled as left parenthesis 2 x plus 3 right parenthesis degrees. The angle between the second and third rays is labeled as left parenthesis x minus 6 right parenthesis degrees.
What is an equation for these two adjacent angles?
(2 points)
(
x+
)° + (x−
)° =
°
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The equation for the two adjacent angles is:
(2x + 3) + (x - 6) = ___°
Simplify by combining like terms:
3x - 3 = ___°
So the equation for the two adjacent angles is:
3x - 3 = ___°
Two adjacent angles, ∠1
and ∠2
, form a resulting angle with measure 135° . If m∠1=(2x)° and m∠2=(2x+7)° , what are the two unknown angle measures?(1 point)
m∠1=
°, m∠2=
°
Given that the sum of the two adjacent angles is 135° and the measures of the angles are m∠1 = (2x)° and m∠2 = (2x + 7)°, we can set up the equation:
m∠1 + m∠2 = 135
Substitute the expressions for m∠1 and m∠2:
(2x) + (2x + 7) = 135
Solve for x:
4x + 7 = 135
4x = 128
x = 32
Then, plug in x back into the expressions for m∠1 and m∠2:
m∠1 = 2(32) = 64°
m∠2 = 2(32) + 7 = 64 + 7 = 71°
Therefore, the two unknown angle measures are:
m∠1 = 64°
m∠2 = 71°
A figure displays two complementary nonadjacent angles. If one of the angles has a measure of 39° , what is the other angle measure?(1 point)
°
Complementary angles add up to 90 degrees.
If one angle has a measure of 39 degrees, the other complementary angle can be found by subtracting this from 90 degrees:
90 - 39 = 51 degrees
Therefore, the other angle measure is 51 degrees.
A figure shows two nonadjacent angles with measures (2x+3)° and 2x° . If the angles are complementary, what is the equation for the angle measures?(1 point)
(
)° + 2x° =
°
Since the angles are complementary, their measures add up to 90 degrees.
The equation for the angle measures is:
(2x + 3) + 2x = 90
Simplify the equation:
2x + 3 + 2x = 90
4x + 3 = 90
So, the equation for the angle measures is:
4x + 3° = 90°
Two complementary angles have measures (2x)° and (3x)° . What is the value of x and the two angle measures?(2 points)
x=
, (2x)°=
°, and (3x)°=
°